Combined and Folded Constructions

Draftsmen frequently draw multiple views of an object, using projection lines to transfer dimensions from one view to another. Consider the building shown at right:

A draftsman would normally want a front view, a top view and a side view. Now we could draw each view separately, measuring dimensions for each view, but why do that when the same dimensions occur in several views? Instead, why not simply draw one view and project the relevant dimensions to the other views, as shown below?

Note that not only can we transfer dimensions between the front view and the other two, but we can transfer dimensions between the top and side views by reflecting them through a diagonal line.

Similar situations arise all the time in structural geology. For example, let's say you need to determine the dip of the layer at right, whose structure contours are given.

The first thing you would do is construct line AB at right angles to the structure contours.

Next, you'd measure out line AB and use the scale to construct a cross-section.

But why measure line AB twice, transferring data from one diagram to another with the possibility of introducing measurement errors? Why not just construct the cross-section using line AB on the map?

Start by constructing AB perpendicular to the contours

Use line AB right on the map to construct the cross-section. That way the contour spacings are transferred directly to the cross-section.

The cross-section plane intersects the map along line AB. What you've done is fold the cross-section along AB into the map plane.